cfd modelling of multi-particulate flow through concentric ......of wellbore drilling. the...

International Journal of Mathematical, Engineering and Management Sciences

Vol. 5, No. 2, 248-259, 2020

https://doi.org/10.33889/IJMEMS.2020.5.2.020

248

CFD Modelling of Multi-Particulate Flow through Concentric Annulus

Satish Kumar Dewangan

Mechanical Engineering Department,

National Institute of Technology, Raipur, 492010, Chhatisgarh, India.

Vivek Deshmukh Mechanical Engineering Department,

National Institute of Technology, Raipur, 492010, Chhatisgarh, India.

Corresponding author: [email protected]

(Received December 26, 2018; Accepted August 31, 2019)

Abstract

In this investigation, flow of multiparticulate lodaded liquid through concentric annulus has been considered with the

consideration of rotating inner wall. The present work guides the research studies for petroleum industries in the field

of wellbore drilling. The hole-cleaning issue is of utmost importance for the wellbore drilling applications. In oil-well

drilling, the horizontal drilling is given more priority. The behaviour of hole cleaning is analyzed through various

parameters like axial inlet flow velocity of particulate flow, inner cylinder rotational speed and inlet solid cuttings

particle concentration. The effect of these aforementioned parameters on the distribution of solid-phase concentration is

studied. Flow is taken as steady, incompressible and multi-particulate slurry flow with primary medium (which carries

the solid phase) being water and silica sand with 6 different sizes as the six different phases. The present flow

simulation has been done by taking the Eulerian approach. The shape of Silica sand is considered as spherical. ANSYS

FLUENT has been used for modelling and solution. Graphs for comparison are obtained using Microsoft Excel.

Keywords- Multi-particulate flow, Concentric annulus, Drilling fluids, Slurry flow, Bed formation.

1. Introduction In various industrial processes, fluids are transported through closed conduits. It is prior to design

the pipe system for the transportation of a specified quantity of fluid between specified locations

with minimum pressure loss considering the initial cost of the piping system. Transportation of

particle laden slurries (through the pipeline) is a commonly seen feature for many variety of

industrial scenerio such as food processing industries, pharmaceuticals manufacturing industries,

chemicals preparation & process industries and mining industries etc. Globally the scientists and

researchers are striving for developing precise models of the velocity profile and solid phase

distribution in a slurry pipeline.

Escudier et al. (2002) studied both the concentric annulus and an eccentric annulus (with 80%

eccentricity ratio) with and without center body (inner wall) rotation for the shear thinning fluid

flow. Nouri and Whitelaw (1997) had considered axial, radial and tangential velocity components

of Newtonian and Non-Newtonian fluid. They concluded that when uniform axial-flow across the

annulus occurs the rotation of inner wall had similar behaviour both for Non-Newtonian and

Newtonian fluids. Kim and Hwang (2003) have simulated a vortex flow inside the annulus. Cruz

and Pinho (2004) researched the concentric annulus with helical flow of fluids considering inner

cylinder rotation. Kelessidis and Bandelis (2004) put forward the concept of coiled tube drilling

which is efficient in the transportation of drill cuttings however it is still in its early stages. Han et

al. (2008, 2009) presented the study of a vertical wellbore system in which the slurry is


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constituted of non-Newtonian fluids loaded with solid cutting particles in a tight annulus. The

effect of annulus angle, the rate of flow, inner wall rotation was seen on solid distribution and

pressure drop. Frigaard and Ngwa (2010) realized that the annular plug fluid was flowing in the

influence of buoyant forces in their analysis considering the Hele-Shaw approximation. Gavrilov

et al. (2011) worked on annular channels having eccentricity considering the rotation of the inner

cylinder. They proposed a numerical algorithm for the simulation of steady, laminar and

incompressible fluid.

In all the studies previously mentioned, the approach to reach a solution is different according to

the type and nature of the flow. Oil and gas industries generally come up with non-Newtonian

flows with turbulent nature. The main role of these fluids is to carry the cuttings generated and

when the boring operation is not working then its role is to make sure that solids remain in the

suspended state. The nature of the flow of slurry is of utmost importance in hole cleaning. The

annular hole is the return passage for slurry and if its cleaning is not done properly then many

adversities can occur. The major challenges in oil-well drilling are premature wearing of rotating

drill bit, pipe sticking, slow rate of drilling, excessive torque, and drag, etc. Hole cleaning can be

made efficient by many parameters like drill string rotation, axial velocity of particulate slurry

flow, drilled hole inclination angle, rate of penetration (ROP), drilling fluid physio-chemical

property and characteristics of solid cuttings generated & its morphology. Moreover, the nature of

solid particles in the slurry influences the life of the bore parts and its performance as well and

because of this many almost all gas and oil-producing houses have to take care of generated

cuttings during the process in addition with oil and gas. This causes several problems such as

cuttings accumulation in lines or equipment, potential damage to reservoir, sand separation

issues, and erosion (Gupta and Pagalthivarthi, 2011).

Figure 1. Geometry and boundary conditions


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2. Problem Definition and Boundary Conditions In the present investigation flow features of sand slurry through a concentric wellbore and various

parameters like inner wall rotation, linear speed of slurry, the concentration of solid particles, size

of solid particles are varied to see the effects on particle size distribution across different planes.

Flow is assumed as three-dimensional, incompressible, steady, and turbulent under the considered

geometrical and kinematic values taken. Geometry and boundary conditions are shown in Figure

1 for the considered case. For the annulus, the outer diameter (Do) is 80 mm, inner diameter (Di)

is 60 mm and length (L) is 1.5 m. Hydraulic mean diameter Dh = (Do - Di ) is 20 mm. Centre of

the inner cylinder is taken as a reference center for measurement. The meshing of the considered

geometry is performed by orthogonal gird for the flow system. A total of 7,14,000 cells has been

generated in the computational domain by the distribution of mesh in radial, axial and azimuthal

direction. The distribution of finally considered mesh was 50×150×120 (radial × azimuthal ×

longitudinal, respectively). Simulation is performed in ANSYS-FLUENT using segregated

solver. Unlike the coupled solver where the equations are solved in a coupled manner in the

segregated solver, equations are solved sequentially.

3. Mathematical and Numerical Methodology In Eulerian model of multiphase flow n set of equation for momentum and continuity is solved

for each phase. Coupling is achieved through the pressure and interphase change coefficient. The

coupling depends upon the type of phases involved whether it is granular flow (fluid-solid) or

non-granular flow (fluid-fluid). The governing equations for a two-fluid model with two

continuous phases are shown below.

𝜕𝛼𝑘𝜌𝑘

𝜕𝑡 + ∇. (𝛼𝑘𝜌𝑘𝑢𝑘) = 0 (1)

𝜕𝛼𝑘𝜌𝑘𝑢𝑘

𝜕𝑡 + ∇. (𝛼𝑘𝜌𝑘𝑢𝑘𝑢𝑘) = 𝜌𝑘𝐶𝑘𝛼𝑘∇𝑃 +𝛼𝑘∇. 𝜏𝑘 +(𝛼𝑘𝜌𝑘𝑔𝑘)+𝑆𝑘=0 (2)

𝜕𝛼𝑘

𝜕𝑡 + ∇. (𝛼𝑘𝑢𝑘) = 0 (3)

In the above equations, 𝑢 represents the mean velocity field, ρ represents density, 𝛼 represents the

volume fraction of the phase and P is the mean pressure shared by the phases. The subscript k

refers to the kth continuous phase. The pipe was first designed in Solid works and then imported to

ANSYS workbench. Meshing is done and various zones (inlet, outlet, inner wall, outer wall) were

recognized. Present study employs RNG k-∈ turbulence model, because it deals very well with

the swirling nature of fluid flow. Longtime researches have proved that this is the best model for

the study of slurry flow (Pagalthivarthi and Gupta, 2009; Kaushal et al., 2013; Dewangan and

Sinha, 2016). For the better study of the regions near thewall, the enhanced wall treatment option

was activated. A total of seven phase have been considered which are:

a. Water (Carrier Phase); Density = 998 kg/m3 , Viscosity = 0.001003 kg/m-s

b. Silica Sand ( 6 Phases of different sizes); Density = 2650 kg/m3 (Refer Table 1).


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Table 1. List of cases used for parametric studies of solid concentration

Case dp(μm) % Cavg Ck % age of Cavg ReH ROH

W3 750, 500, 250,

150, 100, 50

8, 12, 18 5, 10, 15, 15, 25,30 1.75E5 0.02, 0.04, 0.06, 0.08,

0.10, 0.12

W4 750, 500, 250, 150,

100, 50

12 20, 20, 20, 15, 15, 10

1.75E5 0.04, 0.08, 0.12

W5 900, 700,

400, 200, 125, 40

12 10, 15, 15,

15, 20, 25

1.75E5 0.04, 0.08, 0.12

W6 900, 700, 400, 200,

125, 40

12 16.67, 16.67, 16,67, 16.67,

16.67, 16.67

1.75E5 0.04, 0.08, 0.12

W7 738, 255,

180, 128, 91, 38

12 5, 10, 20, 40, 10, 5 1.75E5 0.04, 0.08, 0.12

W8 738, 255, 180, 128,

91, 38

12 5, 15, 30, 30, 10, 10 1.75E5 0.04, 0.08, 0.12

W9 750, 500,

250, 150, 100, 50

12 5,10, 15,15, 25, 30 1.75E5, 2.5E5,

3.5E5, 5E5

0.04

In Table 1,dp represents the particle size diameter, Re represents the linear Reynolds number and

Ro represents the ratio of rotational Reynolds number to Re

ReH = ρvd

µ (4)

ROH = ρωR2

μ∗ReH (5)

4. Results and Discussion The present analysis has targeted the major problem of the horizontal drilling process, which is

the accumulation of cuttings on the lower portion of the hole as this becomes a source of

multitudes of drilling defects. Parameters of input and output have been selected as per this

consideration only. When the solid particles in the slurry do not get a chance to settle down then

it is the only way for thinning of cuttings bed formation. Detailed results considering concentric

annulus with inner cylinder rotation for water–sand slurry flow has been presented here. In the

present work, the variation of concentration of different solid phases is studied with a change in

few crucial parameters such as bulk axial flow velocity (linear velocity) of slurry, rotational speed

of inner pipe, and particle size of the solid phases etc.


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Figure 2. Locations of the radial planes P1, P2, P3 and P4

For insight into simulation within the flow geometry, a cross-section plane at Z = 1.1m is taken

and four radial planes are selected along four perpendicular directions as shown in Figure 2.

Various cases (Table 1) were run in ANSYS Fluent.

4.1 Effect of Slurry Flow Velocity on the Volume Concentration W9 slurry is simulated with different Re values that denote variation in axial velocities.From

equation number 4, velocities calculated are : V1 = 7.78 m/s (corresponding to Re1), V2 = 11.58

m/s (corresponding to Re2), V3 = 15.55 m/s (corresponding to Re3) and V4 = 22.25 m/s

(corresponding to Re4).

Figure 3. Variation of solid phase volume fraction (for W9 slurry) for different slurry velocities at constant

RPM of inner wall along plane 1


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From Figures 3-6, it is observed along plane 1 and plane 3, the volume concentration is maximum

towards the wall and minimum at the center of the annulus. Along with plane 2 and plane 4,

gravity comes into effect and the solid concentration is maximum towards the lower portion of

the annulus. As the velocity decreases, the concentration at the bottom of annulus increases. The

pattern of solid concentration is similar across plane 1 and 3 and also for plane 2 and 4 hence the

results are plotted for plane 1 and 4 in the next investigations.


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4.2 Effect of Solid Phase Particle Diameter on the Volume Concentration The average diameter of solid particles has a great impact on the distribution of particles across

the cross-section of the annulus

Figure 7. Variation of solid phase volume fraction for particle sizes along plane 1


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Figure 8. Variation of solid phase volume fraction for particle sizes along plane 4

It is seen in Figures 7-8 that the pattern of volume concentration along the plane is the same for

plane 1 and plane 3. The pattern of volume concentration along the is same for plane 2 and plane

4 in reverse direction (because of gravity). Along all the four planes as the average diameter

increases, the concentration increases towards the center and for lower diameters volume

concentration is high at the walls. The possible reason can be the momentum effect. As the size

increases, the mass also increases and due to inner rotation of the wall, solid particles accumulate

towards the center which prevents settling at walls.

4.3 Effect of Rotation of Inner Wall Of Annulus on the Volume Concentration

Figure 9. Comparison of solid phase volume fraction for the different rotational speed of inner wall at

constant linear velocity [ROH =0.04 (70 RPM); ROH =0.12 (200 RPM)]


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Linear velocity, size of phases being same, volume concentration (fraction) is compared across

plane 2 and according to the graph shown in Figure 9, one can conclude that as the rotational

speed of inner wall speed increases the phases are more concentrated at the center of the annulus

rather than being concentrated at the inner wall due to gravity. Thus higher the rotation speed of

the inner wall settling down phenomenon will decrease but there is an upper limit to the RPM

which is decided by the system capacity and requirements.

4.4 Effect of Initial Solid Phase Concentration of a Slurry Sample W3 [I.E. for

Constant Particle Diameter Dw] on the Solid Phase Volume Concentration

Distribution As the solid phase percentage is increased in the slurry it is predictable that the volume

concentration of solid particles will also increase in the proportional amount but the nature of the

distribution along the cross-sectional area will be nearly same for all the value of solid phase

percentages.Following graphs are plotted for different percentages of solid concentration for ROH

= 0.02 (33 RPM). Figures 10-11 show the graphs for W3 slurry with ROH = 0.02 (33 RPM) and

linear velocity is also constant i.e. 7.78m/s.

Figure 10. Comparison of solid phase volume fraction for different initial solid phase concentration in

slurry sample W3 for ROH = 0.02 (33 RPM) and constant V = 7.78 m/s along Plane 1


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The only thing varying is the solid-phase content in the slurry. The nature of the concentration

distribution of the solid phase across the cross section is the same for all the three percentages of

solid concentration. As the percentage concentration increases in the slurry, the volume fractions

of solid particles also increase in the proportional amount.




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The above curves are for W3 slurry with ROH = 0.08 (132 RPM) and linear velocity is also

constant i.e. 7.78m/s. The only thing varying is the solid-phase content in the slurry. It is clearly

seen from Figures 12-13 along plane 1 that with the increases in rotational speed of the inner

wall, the volume fraction near the inner wall decreases and happen same for all the percentage

concentration of solid phase. Along plane 4, the volume fraction increases towards the outer wall

for larger RPM because of the combined effect of gravity and centrifugal force on solid particles.

5. Conclusions The overall conclusion is as follow:

As the slurry velocity decreases the concentration at the bottom of annulus increases for W9

slurry ( RPM =200)

The concentration increases towards the center and for lower diameter volume concentration

is high at the walls (V= 7.78 m/s, RPM =200) when the average diameter increases.

As the rotational speed of inner wall increases the phases are more concentrated at the center

of the annulus rather than being concentrated at the inner wall due to gravity. Higher the

rotation speed of the inner wall more the settling down phenomenon.

When the percentage initial solid concentration increases in the slurry at the inlet, the volume

fraction of solid particles also increase in the proportional amount.

Conflict of Interest

The authors confirm that there is no potential conflicts of interest with respect to the research, authorship, and/or

publication of this article.


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Acknowledgments

The authors are grateful to the NIT Raipur (C.G.) India for all letting us to avail the facility of the ANSYS FLUENT

software in the computer lab for the simulation and Institute library.

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Original content of this work is copyright © International Journal of Mathematical, Engineering and Management Sciences. Uses

under the Creative Commons Attribution 4.0 International (CC BY 4.0) license at https://creativecommons.org/licenses/by/4.0/

http://dx.doi.org/10.2118/81746-PA

cfd modelling of multi-particulate flow through concentric ......of wellbore drilling. the...

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